In a GNSS, a receiver estimates delays τ in the navigation signals received from different satellites and uses this information, combined with information on the position of the satellites, to estimate its position. The more accurate the estimation of the delays τ, the more accurately the receiver can estimate its position.
The United States led Global Positioning System (GPS) is presently the GNSS in most common use. Navigation signals transmitted by GPS satellites are modulated using a Phase Shift Keying (PSK) modulation of a code onto a carrier signal having a designated carrier frequency. The modulation involves altering the phase of the carrier signal by fixed amounts (0 or π) at a code rate fC, each symbol of the code having duration TC=1/fC and the code being repeated with time period TG. A navigation signal received at a receiver from a satellite can therefore be represented by an equivalent bi-modal amplitude modulation function α(t−τ)ε(−1,+1) with period TG, as shown in FIG. 1.
The receiver estimates the delay τ by comparing the received signal to a locally generated reference signal. The reference signal consists of an in-phase and quadrature-phase (I and Q) carrier modulated with the same code as the input signal. The reference modulation can be represented mathematically as a(t−{circumflex over (τ)}) where {circumflex over (τ)} is a trial delay. The comparison typically consists in multiplying the received signal by the I and Q reference to yield a demodulated signal. The demodulated signal is then integrated over a given time, usually the same as the period TG of the code, to output a value known as a correlation. The correlation depends on the difference between the trial delay {circumflex over (τ)} of the reference signal and the true delay τ of the received signal and can be expressed as a correlation function Λ({circumflex over (τ)}−τ). As shown in FIG. 2, this correlation function for a PSK modulated signal is triangular and peaks when the trial delay {circumflex over (τ)} matches the true delay τ The width of the correlation function is twice the symbol duration TC, i.e. 2TC.
Calculating the entire correlation function Λ({circumflex over (τ)}−τ) over all {circumflex over (τ)} and analysing it to determine its peak and hence identify the delay τ of the received signal is a computationally time-consuming task. Most conventional GPS receivers therefore compute just three sampled correlations simultaneously, using three reference signals offset in time from one another. The three correlations are usually referred to as gate values of Early (E), Prompt (P) and Late (L) gates. The E and L gates are offset from one another by a time separation TDC, so that they can be considered to have trial delays
      τ    ^    -                    T        DC            2        ⁢                  ⁢    and    ⁢                  ⁢          τ      ^        +            T      DC        2  respectively. The P gate can then be considered to have trial delay {circumflex over (τ)} half way between these trial delays of the E and L gates. So, as illustrated in FIG. 2, when the E and L gate values are equal, the P gate value yields the peak value of the correlation function Λ({circumflex over (τ)}−τ) and the trial delay {circumflex over (τ)} is equal to the true delay τ.
An iterative algorithm can be used to arrive at this state. When the trial delay {circumflex over (τ)} is not equal to the true delay, the P gate will be offset from the peak of the correlation function Λ( ) and there will be a difference in the values of the E and L gates. So, an error signal proportional to the difference between the trial delay {circumflex over (τ)} and the true delay τ can be generated by subtracting the E gate value from the L gate value. This can be used to iteratively adjust the trial delay {circumflex over (τ)} toward the true delay τ. A best estimate of the true delay is then deemed to be the value of the trial delay (of the P gate) when the E gate value is equal to the L gate value (as shown in FIG. 2).
It is presently intended to improve the American GPS by adding new navigation signals to the system. The independent European Galileo system will use similar new navigation signals in both the same and new frequency bands. While some of the new navigation signals will continue to use PSK modulation, most of them will be modulated using the new Binary Offset Carrier (BOC) modulation which is described first. An important sub-set of BOC is called Multiplexed binary offset carrier and is described next.
BOC Modulation.
BOC modulation is like PSK in that it involves modulating a code onto a carrier. The code is similar to that used in PSK modulation, and the code in the received signal can again be represented by an equivalent bi-modal amplitude modulation function a(t−τ) having code rate fC, symbol duration TC and periodicity TG. However, BOC involves further modulating the signal by a sub-carrier, which can be represented by a sub-carrier modulation function s(t−τ) having sub-carrier rate fs and sub-symbol duration equivalent to a half-cycle TS=1/(2fS). As seen in FIG. 3, the sub-carrier modulation function s(t−τ) is a simple periodic square waveform. The sub-carrier rate fs is an integer multiple, or an integer-and-a-half multiple of the code rate fC. The standard notation for BOC modulation reads BOC(fs, fC). This figure shows what can be called ‘sine-BOC’ where the sub carrier has 0 deg phase shift relative to the code zero crossings. Also there is ‘cosine-BOC’ where the sub-carrier is phase shifted 90 deg relative to the code zero-crossings (not shown).
When a received BOC signal is correlated using a matching locally generated BOC reference signal the resulting correlation function ({circumflex over (τ)}−τ) has multiple peaks. For example, referring to FIG. 4a, this correlation function of a sine-BOC signal modulated using BOC(2f, f) has three positive peaks and four negative peaks. The central positive peak corresponds to a match of the true delay τ of the received signal with the trial delay of the reference signal. The other, secondary peaks are separated at intervals of the sub-symbol duration Ts. Importantly, the envelope (dashed line) of this correlation function ({circumflex over (τ)}−τ) is the same as the correlation function Λ({circumflex over (τ)}−τ) of a PSK modulated signal having the same code rate fC.
Because the central peak of the BOC correlation function ({circumflex over (τ)}−τ) has steeper sides than the peak of the equivalent PSK correlation function Λ({circumflex over (τ)}−τ), BOC modulation has the potential to allow more accurate delay estimation. Specifically, when the E and L gates are located on either side of the central peak then the error signal generated from the difference between the L gate value and the E gate value can steer the P gate to the top of the central peak and hence the trial delay {circumflex over (τ)} to the true delay τ, as illustrated in the top part of FIG. 4a. There is however an inherent ambiguity in the delay estimate for a BOC signal provided by the conventional delay estimation technique, as described above. When the E and L gates reside on either side of one of the secondary peaks, the error signal will steer the P gate to the secondary peak (which can be negative). In that situation, the error signal will be zero, just as it is when the P gate is at the top of the central peak, and the iteration will have converged to a value of the trial delay {circumflex over (τ)} that does not correspond to the true delay τ. This is known as ‘false lock’ or ‘slip’, or ‘false node tracking’.
A number of techniques have been proposed for overcoming this problem with pure BOC. One such technique, commonly referred to as ‘bump jumping’, is described in the paper “Tracking Algorithm for GPS Offset Carrier Signals”, P. Fine et al, Proceedings of ION 1999 National Technical Meeting, January 1999. This technique takes advantage of the knowledge that adjacent peaks of the BOC correlation function ({circumflex over (τ)}−τ) are separated from one another by the known sub-carrier symbol duration Ts. Specifically, the technique tests for correct location of the P gate using a pair of gates, called Very Early (VE) and Very Late (VL) gates, having trial delays {circumflex over (τ)}−TS and {circumflex over (τ)}+TS respectively. These are offset from the trial delay {circumflex over (τ)} of the P gate by the sub-carrier symbol duration TS. So, if the P gate has converged to the top of one of the peaks, e.g. the receiver is in lock, the VE, P and VL gates are located on three adjacent peaks. At this stage, the VE, P and VL gate values are compared. If the VE and VL gate amplitudes are less than the P gate amplitude, the P gate is known to lie on the central peak and the trial delay {circumflex over (τ)} corresponds to the true delay. However, if the VE or VL gate amplitude is higher than the P gate value, the P gate is on a secondary peak. In this event, the trial delay {circumflex over (τ)} is incremented by the sub-symbol duration Ts in the direction of whichever of the VE and VL gates has the higher (modulus) value. This action should cause the P gate to jump to the next peak toward the central peak. The comparison is then repeated to verify that the P gate is on the central peak or to cause repeated incrementing of the trial delay {circumflex over (τ)} until the P gate is located on the central peak.
Bump jumping allows a receiver to fully exploit the potential accuracy of BOC. However, there can be a significant waiting time before the delay estimate can be relied on. There is an elapsed time required to decide whether there is a false lock or not. This is longer for a low C/N0, when the VE, P and VL gate values must also be averaged over a significant time in order to be sure which of the three tested adjacent peaks has the highest amplitude. The required time to detect false lock also increases proportionally with the ratio of the sub-carrier rate to the code rate fS/fC, because the difference of amplitude between adjacent peaks relatively decreases. It may also be necessary to correct false lock several times over successive secondary peaks before the central peak is found, a problem which is exacerbated as the ratio of the sub-carrier rate to the code rate fS/fC increases, because the number of secondary peaks increases. Overall, the waiting time may range upwards to several seconds, which is certainly enough to have potentially disastrous consequences for a plane landing, ship docking or such like. Worse, the receiver does not know that it has been in a false lock state until it actually jumps out of it. The bump jumping system therefore is not fail safe.
A further difficulty has now been realised since the launch of the first test satellite GIOVE-A transmitting BOC signals in December 2005. Non-linear and linear distortion in the transmitting chain can easily cause appreciable asymmetry in the actual correlation function ({circumflex over (τ)}−τ)—where the corresponding secondary peaks on either side of the main peak are no longer equal in amplitude. This inevitably degrades performance, and in a worst case, the bump-jumping receiver simply does not work. Recent practical tests are described in “GIOVE-A in orbit testing results” M. Falcone, M. Lugert, M. Malik, M. Crisic, C. Jackson, E. Rooney, M. Trethey ION GNSS FortWorth Tex., September 2006.
FIG. 4b is a simulation of the effect of extreme phase distortion (90 deg). It shows that the later (negative) secondary peak has the same amplitude as the (positive) primary peak. In such a case the VEVL receiver must fail. For less extreme phase distortion—the unbalancing must degrade signal to noise performance, simply because it brings the amplitude of one of the secondary peaks closer to the amplitude of the primary peak.
The paper “Unambiguous Tracker for GPS Binary-Offset-Carrier Signals”, Fante R., ION 59th Annual Meeting/CIGTF 22nd Guidance Test Symposium, 23-25 Jun. 2003, Albuquerque, N. Mex., describes another technique involving multiple sampling (gating) of the correlation function and then linear combination of these samples to synthesise a monotonic approximation to the PSK correlation function Λ({circumflex over (τ)}−τ) having no multiple peaks. This solution certainly eliminates false locks. However, this technique relies on a very complex receiver design. More fundamentally, it fails to realise the potential accuracy conferred by BOC modulation, because the shallower PSK correlation peak is relied on to resolve the delay estimate. Similarly, the paper “BOC(x, y) signal acquisition techniques and performances”, Martin et al., Proceedings of ION GPS 2003, September 2003, Portland, Oreg., describes a technique that exploits the fact that the BOC modulated signal has a mathematical equivalence to two PSK modulated signals centred on two separate carrier frequencies; where the higher frequency fH is equal to the carrier frequency plus the sub-carrier frequency fS while the lower frequency fL is equal to the carrier frequency minus the sub-carrier frequency fS. With appropriate processing the actual monotonic PSK correlation function) Λ({circumflex over (τ)}−τ) can be recovered. But this method is again complex to implement and more fundamentally fails to realise the potential accuracy conferred by BOC modulation.
The solution—described in detail in patent application GB0624516.1—is to eliminate the problem by eliminating the correlation ( ). Instead, a two dimensional correlation is tracked independently to realise a dual estimate. An unambiguous lower accuracy estimate derived from the code phase is used to make an integer correction to a higher accuracy but ambiguous independent estimate based on the sub-carrier phase. The actual receiver may adopt a triple loop, instead of the usual double loop, where carrier phase, sub-carrier phase and code phase are tracked independently but interactively.MBOC Modulation.
Multiplexed binary offset carrier (MBOC) has been proposed in an important modification of BOC. See “MBOC—the new optimized spreading modulation recommended for L1 O and GP L1C” published May/June 2006 Inside GNSS. The proposal is authored and agreed by international experts G. W. Hein, J-Avial Rodriguez, S Wallner, J. W. Betz, C. J. Hegarty, J. J. Rushanan A. L. Kraay, A. R. Pratt, S. Lenahan, J. Owen, J-L Issler and T. Stansell. When adopted it will add a further layer of complexity to reception of GNSS signals compared to ordinary BOC modulation, which is in turn more complicated than PSK modulation. It offers improved accuracy and better rejection of multi-path.
The basis is to make the sub-carrier modulation a linear superposition of BOC(1,1) and BOC(6,1). A common agreed code is described as MBOC(6,1,1/11). The notation implies that 1/11 of the total power is the BOC(6,1) component—and 10/11 of the power is the BOC(1,1) component. The linear superposition can be done by time domain multiplexing where 1/11 of the BOC(1,1) symbols are replaced by BOC(6,1) symbols (same chip width TC=1 μs) having same amplitude (TMBOC). The currently favoured alternative is in the frequency domain multiplexing where there is continuous modulation with unequal amplitudes of the two components (CBOC). Whichever form is adopted makes no difference to the invention. Current proposals divide power into data channel and pilot channel. One current proposal assumes a 50-50 division of power and with no BOC(6,1) component in the data channel, putting it all in the pilot channel. On that basis then the relative proportions of the two components in the pilot channel is 9/11 of BOC(1,1) and 2/11 of BOC(6,1) for which an example is shown in FIG. 5. Whatever proportions are finally decided makes no difference to the invention.
The difference from BOC is clearly seen in the form of a doubly periodic modulation with half periods described by two different sub-chip widths TS1 and TS2. When recovered in the conventional single estimate receiver an even more complicated correlation function as in FIG. 6a is the result. We shall adopt the notation ( ) for the correlation function. Not only are there two secondary (negative) peaks but there are also multiple tertiary peaks. In comparison with the ordinary correlation function for BOC(1,1)—shown as dotted—the slope magnitudes either side of the main peak are higher—which quantifies as an improved accuracy if tracking is correct. But clearly the new modulation offers many more opportunities for false tracking on the ‘ripples’ in the correlation function—for example as in FIG. 6b, when the gate width is narrow, as it has to be for potentially accurate tracking. These figures are for ideal shapes with no phase distortion. As might be expected the new MBOC is more sensitive to phase distortion than BOC. The synthesised effect of phase distortion is shown in FIG. 6c (with 50 deg distortion on BOC(6,1,1/11) where it is clear that the correlation function cannot be tracked because there is a secondary peak equal in amplitude to the primary peak. The complexities of equalization will be needed therefore in order to realize an adequately symmetrical function. At the present time MBOC is so new that no proposals have been published on how to design a receiver to overcome the problems that this complex modulation will entail.
The present invention overcomes the problem of tracking MBOC. The solution is to eliminate the problem by eliminating the correlation function ( ). Instead, a three dimensional correlation is tracked independently to realise a triple estimate. An unambiguous lower accuracy estimate derived from the code phase is used to make an integer correction to a higher accuracy but ambiguous independent estimate based on the lower frequency sub-carrier phase which in turn is used to make an integer correction to even higher accuracy but ambiguous independent estimate based on the higher frequency sub-carrier phase. The actual receiver may adopt a quadruple loop, instead of the usual double loop, where carrier phase, sub-carrier2 phase, sub-carrier1 phase and code phase are tracked independently but interactively.